Using the two-field reduced magneto-hydrodynamic (MHD) model, a new theory of tearing mode transition from linear to Rutherford regime in the presence of local equilibrium current gradient (LCG) effects is proposed. By containing the LCG term in the vorticity equation, I reproduce the modified Rutherford equation with saturation terms via a quasi-linear approach. Therefore, the LCG term in the vorticity equation is responsible for the saturation mechanism of the classical tearing mode. The unified formula of the tearing mode evolution from linear exponential growth to quasi-linear saturation is obtained if one contains the LCG and inertial terms in the vorticity equation simultaneously. Since LCG is essential for the linear growth rate of tearing mode in the marginal stable regime, the new theory is also valid when the mode close to marginality.